Large-scale page recommendations on online social networks

ABSTRACT

In one embodiment, a method includes accessing user-concept scores for a first set of users, wherein each user-concept score is associated with a user-concept pair; calculating recommended user-concept scores for a subset of user-concept pairs in a second set of users. The first set of users may be discrete from the second set of users. A recommendation-algorithm may compute the recommended user-concept scores for a user-concept pair by optimizing an objective function comprising a plurality of predicted rating functions. Each predicted rating function may be determined using a user score, a concept score, a user-bias value associated with the user, as well as a concept-bias value associated with the concept. Finally, the method may include sending recommendations for one or more concepts based on the recommended user-concept scores for the second set of users.

PRIORITY

This application is a continuation under 35 U.S.C. § 120 of U.S. patentapplication Ser. No. 13/942,486, filed 15 Jul. 2013.

TECHNICAL FIELD

This disclosure generally relates to online social networks.

BACKGROUND

A social-networking system, which may include a social-networkingwebsite, may enable its users (such as persons or organizations) tointeract with it and with each other through it. The social-networkingsystem may, with input from a user, create and store in thesocial-networking system a user profile associated with the user. Theuser profile may include demographic information, communication-channelinformation, and information on personal interests of the user. Thesocial-networking system may also, with input from a user, create andstore a record of relationships of the user with other users of thesocial-networking system, as well as provide services (e.g., wall posts,photo-sharing, event organization, messaging, games, or advertisements)to facilitate social interaction between or among users.

The social-networking system may send over one or more networks contentor messages related to its services to a mobile or other computingdevice of a user. A user may also install software applications on amobile or other computing device of the user for accessing a userprofile of the user and other data within the social-networking system.The social-networking system may generate a personalized set of contentobjects to display to a user, such as a newsfeed of aggregated storiesof other users connected to the user.

Matrix factorization is a factorization of a matrix into a product ofmatrices. Low-rank matrix factorizations are effective tools foranalysis of dyadic data, which aims at discovering and capturing theinteractions between two entities. Successful applications include topicdetection and keyword search (where the corresponding entities aredocuments and terms), news personalization (users and stories), andrecommendation systems (users and items). In large applications, theseproblems can involve matrices with millions of rows (e.g., distinctcustomers), millions of columns (e.g., distinct items), and billions ofentries (e.g., interactions between customers and items).

SUMMARY OF PARTICULAR EMBODIMENTS

In particular embodiments, the social-networking system may identifycontent objects to recommend or advertise to large numbers of users ofan online social network. Such recommendations may be identified inorder to optimize the conversion rate of content presented to users.Content recommendations may be determined by optimizing an objectivefunction comprising predicted rating functions, wherein each ratingfunction (for a user-concept pair) comprises a dot product of auser-score vector and a concept-score vector, and bias values. However,computing the dot product of these vectors for all users of the onlinesocial network directly may be prohibitive from a time and processingperspective. In particular embodiments, the social-networking system maypredict interests of a user through collaborative filtering based onconnections to entities provided by the user, and leverage theseinterests to make content recommendations. The online social network maybe associated with more than a billion users and many millions ofconcepts (e.g., places, websites, entities, resources, etc.), where itmay be desirable to recommend these users and concepts to other users.Instead of using rating data from all users and all concepts, which maybe an unfeasibly large data set, the social-networking system may userating data from only a sample of users with respect to all conceptsassociated with the online social network, and use this limited data setto calculate the concept traits. These concept traits may then be fixedand used to calculate user traits for all remaining users of the onlinesocial network. After getting user traits and concept traits, instead ofcalculating the scores directly for each user-concept pair, thesocial-networking system may use random projection to scope down theconcepts for every user. It may determine the most similar concepts forevery concept based on cosine similarity distance of the concept traitvectors, and then use that as source to provide suggestions to users(e.g., concepts most similar to one the user has previously “liked” orotherwise interacted with).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example network environment associated with asocial-networking system.

FIG. 2 illustrates an example social graph.

FIG. 3 illustrates an example method for determining recommended contenton an online social network.

FIG. 4 illustrates an example computer system.

DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 illustrates an example network environment 100 associated with asocial-networking system. Network environment 100 includes a clientsystem 130, a social-networking system 160, and a third-party system 170connected to each other by a network 110. Although FIG. 1 illustrates aparticular arrangement of client system 130, social-networking system160, third-party system 170, and network 110, this disclosurecontemplates any suitable arrangement of client system 130,social-networking system 160, third-party system 170, and network 110.As an example and not by way of limitation, two or more of client system130, social-networking system 160, and third-party system 170 may beconnected to each other directly, bypassing network 110. As anotherexample, two or more of client system 130, social-networking system 160,and third-party system 170 may be physically or logically co-locatedwith each other in whole or in part. Moreover, although FIG. 1illustrates a particular number of client systems 130, social-networkingsystems 160, third-party systems 170, and networks 110, this disclosurecontemplates any suitable number of client systems 130,social-networking systems 160, third-party systems 170, and networks110. As an example and not by way of limitation, network environment 100may include multiple client system 130, social-networking systems 160,third-party systems 170, and networks 110.

This disclosure contemplates any suitable network 110. As an example andnot by way of limitation, one or more portions of network 110 mayinclude an ad hoc network, an intranet, an extranet, a virtual privatenetwork (VPN), a local area network (LAN), a wireless LAN (WLAN), a widearea network (WAN), a wireless WAN (WWAN), a metropolitan area network(MAN), a portion of the Internet, a portion of the Public SwitchedTelephone Network (PSTN), a cellular telephone network, or a combinationof two or more of these. Network 110 may include one or more networks110.

Links 150 may connect client system 130, social-networking system 160,and third-party system 170 to communication network 110 or to eachother. This disclosure contemplates any suitable links 150. Inparticular embodiments, one or more links 150 include one or morewireline (such as for example Digital Subscriber Line (DSL) or Data OverCable Service Interface Specification (DOCSIS)), wireless (such as forexample Wi-Fi or Worldwide Interoperability for Microwave Access(WiMAX)), or optical (such as for example Synchronous Optical Network(SONET) or Synchronous Digital Hierarchy (SDH)) links. In particularembodiments, one or more links 150 each include an ad hoc network, anintranet, an extranet, a VPN, a LAN, a WLAN, a WAN, a WWAN, a MAN, aportion of the Internet, a portion of the PSTN, a cellulartechnology-based network, a satellite communications technology-basednetwork, another link 150, or a combination of two or more such links150. Links 150 need not necessarily be the same throughout networkenvironment 100. One or more first links 150 may differ in one or morerespects from one or more second links 150.

In particular embodiments, client system 130 may be an electronic deviceincluding hardware, software, or embedded logic components or acombination of two or more such components and capable of carrying outthe appropriate functionalities implemented or supported by clientsystem 130. As an example and not by way of limitation, a client system130 may include a computer system such as a desktop computer, notebookor laptop computer, netbook, a tablet computer, e-book reader, GPSdevice, camera, personal digital assistant (PDA), handheld electronicdevice, cellular telephone, smartphone, other suitable electronicdevice, or any suitable combination thereof. This disclosurecontemplates any suitable client systems 130. A client system 130 mayenable a network user at client system 130 to access network 110. Aclient system 130 may enable its user to communicate with other users atother client systems 130.

In particular embodiments, client system 130 may include a web browser132, such as MICROSOFT INTERNET EXPLORER, GOOGLE CHROME or MOZILLAFIREFOX, and may have one or more add-ons, plug-ins, or otherextensions, such as TOOLBAR or YAHOO TOOLBAR. A user at client system130 may enter a Uniform Resource Locator (URL) or other addressdirecting the web browser 132 to a particular server (such as server162, or a server associated with a third-party system 170), and the webbrowser 132 may generate a Hyper Text Transfer Protocol (HTTP) requestand communicate the HTTP request to server. The server may accept theHTTP request and communicate to client system 130 one or more Hyper TextMarkup Language (HTML) files responsive to the HTTP request. Clientsystem 130 may render a webpage based on the HTML files from the serverfor presentation to the user. This disclosure contemplates any suitablewebpage files. As an example and not by way of limitation, webpages mayrender from HTML files, Extensible Hyper Text Markup Language (XHTML)files, or Extensible Markup Language (XML) files, according toparticular needs. Such pages may also execute scripts such as, forexample and without limitation, those written in JAVASCRIPT, JAVA,MICROSOFT SILVERLIGHT, combinations of markup language and scripts suchas AJAX (Asynchronous JAVASCRIPT and XML), and the like. Herein,reference to a webpage encompasses one or more corresponding webpagefiles (which a browser may use to render the webpage) and vice versa,where appropriate.

In particular embodiments, social-networking system 160 may be anetwork-addressable computing system that can host an online socialnetwork. Social-networking system 160 may generate, store, receive, andsend social-networking data, such as, for example, user-profile data,concept-profile data, social-graph information, or other suitable datarelated to the online social network. Social-networking system 160 maybe accessed by the other components of network environment 100 eitherdirectly or via network 110. In particular embodiments,social-networking system 160 may include one or more servers 162. Eachserver 162 may be a unitary server or a distributed server spanningmultiple computers or multiple datacenters. Servers 162 may be ofvarious types, such as, for example and without limitation, web server,news server, mail server, message server, advertising server, fileserver, application server, exchange server, database server, proxyserver, another server suitable for performing functions or processesdescribed herein, or any combination thereof. In particular embodiments,each server 162 may include hardware, software, or embedded logiccomponents or a combination of two or more such components for carryingout the appropriate functionalities implemented or supported by server162. In particular embodiments, social-networking system 164 may includeone or more data stores 164. Data stores 164 may be used to storevarious types of information. In particular embodiments, the informationstored in data stores 164 may be organized according to specific datastructures. In particular embodiments, each data store 164 may be arelational, columnar, correlation, or other suitable database. Althoughthis disclosure describes or illustrates particular types of databases,this disclosure contemplates any suitable types of databases. Particularembodiments may provide interfaces that enable a client system 130, asocial-networking system 160, or a third-party system 170 to manage,retrieve, modify, add, or delete, the information stored in data store164.

In particular embodiments, social-networking system 160 may store one ormore social graphs in one or more data stores 164. In particularembodiments, a social graph may include multiple nodes—which may includemultiple user nodes (each corresponding to a particular user) ormultiple concept nodes (each corresponding to a particular concept)—andmultiple edges connecting the nodes. Social-networking system 160 mayprovide users of the online social network the ability to communicateand interact with other users. In particular embodiments, users may jointhe online social network via social-networking system 160 and then addconnections (e.g., relationships) to a number of other users ofsocial-networking system 160 whom they want to be connected to. Herein,the term “friend” may refer to any other user of social-networkingsystem 160 with whom a user has formed a connection, association, orrelationship via social-networking system 160.

In particular embodiments, social-networking system 160 may provideusers with the ability to take actions on various types of items orobjects, supported by social-networking system 160. As an example andnot by way of limitation, the items and objects may include groups orsocial networks to which users of social-networking system 160 maybelong, events or calendar entries in which a user might be interested,computer-based applications that a user may use, transactions that allowusers to buy or sell items via the service, interactions withadvertisements that a user may perform, or other suitable items orobjects. A user may interact with anything that is capable of beingrepresented in social-networking system 160 or by an external system ofthird-party system 170, which is separate from social-networking system160 and coupled to social-networking system 160 via a network 110.

In particular embodiments, social-networking system 160 may be capableof linking a variety of entities. As an example and not by way oflimitation, social-networking system 160 may enable users to interactwith each other as well as receive content from third-party systems 170or other entities, or to allow users to interact with these entitiesthrough an application programming interfaces (API) or othercommunication channels.

In particular embodiments, a third-party system 170 may include one ormore types of servers, one or more data stores, one or more interfaces,including but not limited to APIs, one or more web services, one or morecontent sources, one or more networks, or any other suitable components,e.g., that servers may communicate with. A third-party system 170 may beoperated by a different entity from an entity operatingsocial-networking system 160. In particular embodiments, however,social-networking system 160 and third-party systems 170 may operate inconjunction with each other to provide social-networking services tousers of social-networking system 160 or third-party systems 170. Inthis sense, social-networking system 160 may provide a platform, orbackbone, which other systems, such as third-party systems 170, may useto provide social-networking services and functionality to users acrossthe Internet.

In particular embodiments, a third-party system 170 may include athird-party content object provider. A third-party content objectprovider may include one or more sources of content objects, which maybe communicated to a client system 130. As an example and not by way oflimitation, content objects may include information regarding things oractivities of interest to the user, such as, for example, movie showtimes, movie reviews, restaurant reviews, restaurant menus, productinformation and reviews, or other suitable information. As anotherexample and not by way of limitation, content objects may includeincentive content objects, such as coupons, discount tickets, giftcertificates, or other suitable incentive objects.

In particular embodiments, social-networking system 160 also includesuser-generated content objects, which may enhance a user's interactionswith social-networking system 160. User-generated content may includeanything a user can add, upload, send, or “post” to social-networkingsystem 160. As an example and not by way of limitation, a usercommunicates posts to social-networking system 160 from a client system130. Posts may include data such as status updates or other textualdata, location information, photos, videos, links, music or othersimilar data or media. Content may also be added to social-networkingsystem 160 by a third-party through a “communication channel,” such as anewsfeed or stream.

In particular embodiments, social-networking system 160 may include avariety of servers, sub-systems, programs, modules, logs, and datastores. In particular embodiments, social-networking system 160 mayinclude one or more of the following: a web server, action logger,API-request server, relevance-and-ranking engine, content-objectclassifier, notification controller, action log,third-party-content-object-exposure log, inference module,authorization/privacy server, search module, advertisement-targetingmodule, user-interface module, user-profile store, connection store,third-party content store, or location store. Social-networking system160 may also include suitable components such as network interfaces,security mechanisms, load balancers, failover servers,management-and-network-operations consoles, other suitable components,or any suitable combination thereof. In particular embodiments,social-networking system 160 may include one or more user-profile storesfor storing user profiles. A user profile may include, for example,biographic information, demographic information, behavioral information,social information, or other types of descriptive information, such aswork experience, educational history, hobbies or preferences, interests,affinities, or location. Interest information may include interestsrelated to one or more categories. Categories may be general orspecific. As an example and not by way of limitation, if a user “likes”an article about a brand of shoes the category may be the brand, or thegeneral category of “shoes” or “clothing.” A connection store may beused for storing connection information about users. The connectioninformation may indicate users who have similar or common workexperience, group memberships, hobbies, educational history, or are inany way related or share common attributes. The connection informationmay also include user-defined connections between different users andcontent (both internal and external). A web server may be used forlinking social-networking system 160 to one or more client systems 130or one or more third-party system 170 via network 110. The web servermay include a mail server or other messaging functionality for receivingand routing messages between social-networking system 160 and one ormore client systems 130. An API-request server may allow a third-partysystem 170 to access information from social-networking system 160 bycalling one or more APIs. An action logger may be used to receivecommunications from a web server about a user's actions on or offsocial-networking system 160. In conjunction with the action log, athird-party-content-object log may be maintained of user exposures tothird-party-content objects. A notification controller may provideinformation regarding content objects to a client system 130.Information may be pushed to a client system 130 as notifications, orinformation may be pulled from client system 130 responsive to a requestreceived from client system 130. Authorization servers may be used toenforce one or more privacy settings of the users of social-networkingsystem 160. A privacy setting of a user determines how particularinformation associated with a user can be shared. The authorizationserver may allow users to opt in to or opt out of having their actionslogged by social-networking system 160 or shared with other systems(e.g., third-party system 170), such as, for example, by settingappropriate privacy settings. Third-party-content-object stores may beused to store content objects received from third parties, such as athird-party system 170. Location stores may be used for storing locationinformation received from client systems 130 associated with users.Advertisement-pricing modules may combine social information, thecurrent time, location information, or other suitable information toprovide relevant advertisements, in the form of notifications, to auser.

FIG. 2 illustrates example social graph 200. In particular embodiments,social-networking system 160 may store one or more social graphs 200 inone or more data stores. In particular embodiments, social graph 200 mayinclude multiple nodes—which may include multiple user nodes 202 ormultiple concept nodes 204—and multiple edges 206 connecting the nodes.Example social graph 200 illustrated in FIG. 2 is shown, for didacticpurposes, in a two-dimensional visual map representation. In particularembodiments, a social-networking system 160, client system 130, orthird-party system 170 may access social graph 200 and relatedsocial-graph information for suitable applications. The nodes and edgesof social graph 200 may be stored as data objects, for example, in adata store (such as a social-graph database). Such a data store mayinclude one or more searchable or queryable indexes of nodes or edges ofsocial graph 200.

In particular embodiments, a user node 202 may correspond to a user ofsocial-networking system 160. As an example and not by way oflimitation, a user may be an individual (human user), an entity (e.g.,an enterprise, business, or third-party application), or a group (e.g.,of individuals or entities) that interacts or communicates with or oversocial-networking system 160. In particular embodiments, when a userregisters for an account with social-networking system 160,social-networking system 160 may create a user node 202 corresponding tothe user, and store the user node 202 in one or more data stores. Usersand user nodes 202 described herein may, where appropriate, refer toregistered users and user nodes 202 associated with registered users. Inaddition or as an alternative, users and user nodes 202 described hereinmay, where appropriate, refer to users that have not registered withsocial-networking system 160. In particular embodiments, a user node 202may be associated with information provided by a user or informationgathered by various systems, including social-networking system 160. Asan example and not by way of limitation, a user may provide his or hername, profile picture, contact information, birth date, sex, maritalstatus, family status, employment, education background, preferences,interests, or other demographic information. In particular embodiments,a user node 202 may be associated with one or more data objectscorresponding to information associated with a user. In particularembodiments, a user node 202 may correspond to one or more webpages.

In particular embodiments, a concept node 204 may correspond to aconcept. As an example and not by way of limitation, a concept maycorrespond to a place (such as, for example, a movie theater,restaurant, landmark, or city); a website (such as, for example, awebsite associated with social-network system 160 or a third-partywebsite associated with a web-application server); an entity (such as,for example, a person, business, group, sports team, or celebrity); aresource (such as, for example, an audio file, video file, digitalphoto, text file, structured document, or application) which may belocated within social-networking system 160 or on an external server,such as a web-application server; real or intellectual property (suchas, for example, a sculpture, painting, movie, game, song, idea,photograph, or written work); a game; an activity; an idea or theory;another suitable concept; or two or more such concepts. A concept node204 may be associated with information of a concept provided by a useror information gathered by various systems, including social-networkingsystem 160. As an example and not by way of limitation, information of aconcept may include a name or a title; one or more images (e.g., animage of the cover page of a book); a location (e.g., an address or ageographical location); a website (which may be associated with a URL);contact information (e.g., a phone number or an email address); othersuitable concept information; or any suitable combination of suchinformation. In particular embodiments, a concept node 204 may beassociated with one or more data objects corresponding to informationassociated with concept node 204. In particular embodiments, a conceptnode 204 may correspond to one or more webpages.

In particular embodiments, a node in social graph 200 may represent orbe represented by a webpage (which may be referred to as a “profilepage”). Profile pages may be hosted by or accessible tosocial-networking system 160. Profile pages may also be hosted onthird-party websites associated with a third-party server 170. As anexample and not by way of limitation, a profile page corresponding to aparticular external webpage may be the particular external webpage andthe profile page may correspond to a particular concept node 204.Profile pages may be viewable by all or a selected subset of otherusers. As an example and not by way of limitation, a user node 202 mayhave a corresponding user-profile page in which the corresponding usermay add content, make declarations, or otherwise express himself orherself. As another example and not by way of limitation, a concept node204 may have a corresponding concept-profile page in which one or moreusers may add content, make declarations, or express themselves,particularly in relation to the concept corresponding to concept node204.

In particular embodiments, a concept node 204 may represent athird-party webpage or resource hosted by a third-party system 170. Thethird-party webpage or resource may include, among other elements,content, a selectable or other icon, or other inter-actable object(which may be implemented, for example, in JavaScript, AJAX, or PHPcodes) representing an action or activity. As an example and not by wayof limitation, a third-party webpage may include a selectable icon suchas “like,” “check in,” “eat,” “recommend,” or another suitable action oractivity. A user viewing the third-party webpage may perform an actionby selecting one of the icons (e.g., “eat”), causing a client system 130to send to social-networking system 160 a message indicating the user'saction. In response to the message, social-networking system 160 maycreate an edge (e.g., an “eat” edge) between a user node 202corresponding to the user and a concept node 204 corresponding to thethird-party webpage or resource and store edge 206 in one or more datastores.

In particular embodiments, a pair of nodes in social graph 200 may beconnected to each other by one or more edges 206. An edge 206 connectinga pair of nodes may represent a relationship between the pair of nodes.In particular embodiments, an edge 206 may include or represent one ormore data objects or attributes corresponding to the relationshipbetween a pair of nodes. As an example and not by way of limitation, afirst user may indicate that a second user is a “friend” of the firstuser. In response to this indication, social-networking system 160 maysend a “friend request” to the second user. If the second user confirmsthe “friend request,” social-networking system 160 may create an edge206 connecting the first user's user node 202 to the second user's usernode 202 in social graph 200 and store edge 206 as social-graphinformation in one or more of data stores 164. In the example of FIG. 2,social graph 200 includes an edge 206 indicating a friend relationbetween user nodes 202 of user “A” and user “B” and an edge indicating afriend relation between user nodes 202 of user “C” and user “B.”Although this disclosure describes or illustrates particular edges 206with particular attributes connecting particular user nodes 202, thisdisclosure contemplates any suitable edges 206 with any suitableattributes connecting user nodes 202. As an example and not by way oflimitation, an edge 206 may represent a friendship, family relationship,business or employment relationship, fan relationship, followerrelationship, visitor relationship, subscriber relationship,superior/subordinate relationship, reciprocal relationship,non-reciprocal relationship, another suitable type of relationship, ortwo or more such relationships. Moreover, although this disclosuregenerally describes nodes as being connected, this disclosure alsodescribes users or concepts as being connected. Herein, references tousers or concepts being connected may, where appropriate, refer to thenodes corresponding to those users or concepts being connected in socialgraph 200 by one or more edges 206.

In particular embodiments, an edge 206 between a user node 202 and aconcept node 204 may represent a particular action or activity performedby a user associated with user node 202 toward a concept associated witha concept node 204. As an example and not by way of limitation, asillustrated in FIG. 2, a user may “like,” “attended,” “played,”“listened,” “cooked,” “worked at,” or “watched” a concept, each of whichmay correspond to a edge type or subtype. A concept-profile pagecorresponding to a concept node 204 may include, for example, aselectable “check in” icon (such as, for example, a clickable “check in”icon) or a selectable “add to favorites” icon. Similarly, after a userclicks these icons, social-networking system 160 may create a “favorite”edge or a “check in” edge in response to a user's action correspondingto a respective action. As another example and not by way of limitation,a user (user “C”) may listen to a particular song (“Imagine”) using aparticular application (SPOTIFY, which is an online music application).In this case, social-networking system 160 may create a “listened” edge206 and a “used” edge (as illustrated in FIG. 2) between user nodes 202corresponding to the user and concept nodes 204 corresponding to thesong and application to indicate that the user listened to the song andused the application. Moreover, social-networking system 160 may createa “played” edge 206 (as illustrated in FIG. 2) between concept nodes 204corresponding to the song and the application to indicate that theparticular song was played by the particular application. In this case,“played” edge 206 corresponds to an action performed by an externalapplication (SPOTIFY) on an external audio file (the song “Imagine”).Although this disclosure describes particular edges 206 with particularattributes connecting user nodes 202 and concept nodes 204, thisdisclosure contemplates any suitable edges 206 with any suitableattributes connecting user nodes 202 and concept nodes 204. Moreover,although this disclosure describes edges between a user node 202 and aconcept node 204 representing a single relationship, this disclosurecontemplates edges between a user node 202 and a concept node 204representing one or more relationships. As an example and not by way oflimitation, an edge 206 may represent both that a user likes and hasused at a particular concept. Alternatively, another edge 206 mayrepresent each type of relationship (or multiples of a singlerelationship) between a user node 202 and a concept node 204 (asillustrated in FIG. 2 between user node 202 for user “E” and conceptnode 204 for “SPOTIFY”).

In particular embodiments, social-networking system 160 may create anedge 206 between a user node 202 and a concept node 204 in social graph200. As an example and not by way of limitation, a user viewing aconcept-profile page (such as, for example, by using a web browser or aspecial-purpose application hosted by the user's client system 130) mayindicate that he or she likes the concept represented by the conceptnode 204 by clicking or selecting a “Like” icon, which may cause theuser's client system 130 to send to social-networking system 160 amessage indicating the user's liking of the concept associated with theconcept-profile page. In response to the message, social-networkingsystem 160 may create an edge 206 between user node 202 associated withthe user and concept node 204, as illustrated by “like” edge 206 betweenthe user and concept node 204. In particular embodiments,social-networking system 160 may store an edge 206 in one or more datastores. In particular embodiments, an edge 206 may be automaticallyformed by social-networking system 160 in response to a particular useraction. As an example and not by way of limitation, if a first useruploads a picture, watches a movie, or listens to a song, an edge 206may be formed between user node 202 corresponding to the first user andconcept nodes 204 corresponding to those concepts. Although thisdisclosure describes forming particular edges 206 in particular manners,this disclosure contemplates forming any suitable edges 206 in anysuitable manner.

In particular embodiments, social-networking system 160 may identifycontent objects to recommend or advertise to large numbers of users ofan online social network. These content objects may be user-profilepages, concept-profile pages, multimedia content, advertisements, or anyother suitable objects associated with the online social network. Suchrecommendations may be identified in order to optimize conversion rate(i.e., number of interactions/clicks vs. number of impressions) ofcontent presented to users. Content recommendations may be computed byoptimizing an objective function comprising predicted rating functions,wherein each rating function for a user-concept pair (u,i) comprises adot product of a user-score vector P(u) and a concept-score vector Q(i),and bias values. However, directly computing of the dot product of thesevectors for all users of the online social network may be prohibitivefrom a time and processing perspective. Thus, it may be advantageous toprovide a more efficient way to determine targeted and relevant conceptrecommendations to users based on each user's personal taste. Inparticular embodiments, social-networking system 160 may predictinterests of a user through collaborative filtering based on connectionsto entities provided by the user (e.g., user-generated edge connectionsbetween user nodes 202 and other nodes of social graph 200, which may bereferred to as rating data), and leverage these interests to makecontent recommendations. The challenge is that at the online socialnetwork may be associated with more than a billion users and manymillions of concepts (corresponding to user nodes 202 and concept nodes204, respectively), where it may be desirable to recommend these usersand concepts (e.g., recommend their corresponding profile pages) toother users. Due to the size of the social graph 200, it may beprohibitive to use standard dimension reduction techniques such assingular value decomposition (SVD) to calculate user recommendations dueto time and computational power constraints. Even if the system can geta low-dimensional approximation of users and recommendations, the costof calculating the score of all possible user-concept pairs may beextremely high. As an example and not by way of limitation, for a socialgraph 200 comprising over 1 billion user nodes 202 and 5 millionsconcept nodes 204, it would take over 5 quadrillion (5×10¹⁵)computations to analyze all user-concept pairs, which may be infeasibleto complete within a reasonable timeframe. Even if all concepts can bescored on an individual basis, serving recommendations from such a largeset requires large-scale infrastructure. Therefore, instead of usingrating data from all users and all concepts, which may be an unfeasiblylarge data set, social-networking may use rating data from only a sampleof users (e.g., 1%) with respect to all concepts associated with theonline social network, and use this limited data set to calculate allconcept traits. These concept traits may then be fixed and used tocalculate user traits for all remaining users of the online socialnetwork. After getting user traits and concept traits, instead ofcalculating the scores directly for each user-concept pair,social-networking system 160 may use random projection to scope down theconcepts for every user. It may determine the most similar concepts forevery concept based on cosine similarity distance of the concept traitvectors, and then use that as source to provide suggestions to users(e.g., concepts most similar to one the user has previously “liked” orotherwise interacted with). Although this disclosure describesidentifying particular content objects to recommend or advertise in aparticular manner, this disclosure contemplates identifying any suitablecontent objects to recommend or advertise in any suitable manner.

In particular embodiments, social-networking system 160 may accessuser-concept scores for a first set of user nodes 202 of the pluralityof nodes, respectively. Each user-concept score may be with respect toparticular user-concept pairs comprising a user node 202 from the firstset of user nodes that is connected by an edge 206 to a concept node 204from the plurality of concept nodes. The first set of user nodes 202 maycomprise a representative number of user nodes 202 corresponding to arepresentative sample of users of the online social network. As anexample and not by way of limitation, the first set of user nodes 202may comprise approximately 1% of the user nodes 202 of the plurality ofuser nodes 202 of social graph 200 (although, any other suitablefraction may be used, such as, for example, 0.1%, 1%, 2%, 5%, 10%, oranother suitable fraction of the users of the online social network). Inconnection with identifying and selecting user sets, particularembodiments may utilize one or more systems, components, elements,functions, methods, operations, or steps disclosed in U.S. patentapplication Ser. No. 13/939,093, filed 10 Jul. 2013, which isincorporated by reference. In particular embodiments, social-networkingsystem 160 may access a ratings matrix R representing the user-conceptscores for the first set of user nodes 202. Rating matrix R may compriseratings of users to concepts, where R(u,i) may present the rating fromthe user node u to the concept node i. Ratings matrix R may be generatedby self-reported connections between users and entities (e.g., edge 206connections when a user “likes” a concept). In the context of socialgraph 200, nodes connected by an edge 206 may be considered to have arating/score with respect to the node pair, while unconnected nodes mayhave no score or a null score with respect to the node pair. The ratingsmatrix R may be extremely spare in that the typical user may haverated/liked very few concepts relative to the total number of conceptsassociated with the online social network. In other words, the typicaluser node 202 may be connected by edges 206 to relatively few conceptnodes 204. But a ratings matrix R for all users may have a very largedimensionality if there are, for example, over a billion users andmillions of concepts. Based on the ratings matrix R, social-networkingsystem 160 may then determine a user matrix P, wherein the user matrix Pcomprises a plurality of user-score vectors P(u) for each user node u ofthe first set of users nodes 202. Social-networking system 160 may alsodetermine a concept matrix Q based on the ratings matrix R, wherein theconcept matrix Q comprises a plurality of concept-score vectors Q(i) foreach concept node i of the plurality of concepts nodes. As an exampleand not by way of limitation, social-networking system 160 may take 1%of users and all concepts, collect interaction history (e.g., edge-typeinformation regarding connections user nodes 202 to concept nodes 204)between the 1% users and concepts as training data, and use adistributed stochastic gradient descent algorithm to calculate usertrace vectors for all 1% users and concept trace vectors for allconcepts, and biases for all user-concept pairs. Although thisdisclosure describes accessing particular user-concept scores in aparticular manner, this disclosure contemplates accessing any suitableuser-concept scores in any suitable manner.

In particular embodiments, social-networking system 160 may generate arecommendation-algorithm for estimating recommended user-concept scoresfor all user-concept pairs in the first set of user nodes 202 and theplurality of concept nodes 204. The recommended user-concept scores maybe based on the accessed user-concept scores, as described previously.In particular embodiments, social-networking system 160 may use a matrixfactorization model to allow for the computation of a recommendationscore for every user-concept pair (u,i) by use of user traits andconcept traits. As an example and not by way of limitation,social-networking system 160 may calculate a recommendation score from aratings matrix R. Social-networking system 160 may access a user matrixP based on ratings matrix R, where user matrix P comprises a pluralityof user-score vectors P(u) (also called user trait vectors) for eachuser node u of the first set of user nodes 202, wherein each user node uis associated with a user-bias vector B_(u)(u). In other words, in usermatrix P each row may be indexed by a user and the columns may be valuesin a trait space. The trait space of user matrix P may have dimension k.Social-networking system 160 may then access a concept matrix Q based onratings matrix R, where the concept matrix Q comprises a plurality ofconcept-score vectors Q(i) (also called concept trait vectors) for eachconcept node i of the plurality of concepts, wherein each concept node iis associated with a concept-bias vector B_(i)(i). In other words,concept matrix Q is a matrix where each column is indexed by a conceptand the rows are values in a trait space. The trait space of conceptmatrix Q may have dimension k as well. The columns of concept matrix Qare referenced by concept node i. Every user may have a bias valuedefined by user-bias vector B_(u)(u), where B_(u) is a vector of allbiases of users. Similarly, every concept may have a bias value definedby concept-bias vector B_(i)(i), where B_(i) is a vector of all biasesof concepts. Social-networking system 160 may then generate an estimatormatrix R′ representing recommended user-concept scores for the first setof user nodes, wherein the rating of user node u to concept node i isR′(u,i)=P(u)·Q(i)+B_(u)(u)+B_(i)(i) for each user-concept pair (u,i). Inparticular embodiments, social-networking system 160 may determine theuser matrix P, the user-score vectors P(u) for each user node u, theconcept matrix Q, and the concept-score vectors Q(i) for each conceptnode i using distributed stochastic gradient descent (DSGD). As anexample and not by way of limitation, the implementation algorithm usedby social-networking system 160 may use distributed stochastic gradientdescent to find user matrix P, concept matrix Q, user-bias vectorB_(u)(u), and concept-bias vector B_(i)(i) such that the score/rating ofuser node u and concept node i generated by the formula for R′(u,i) mostclosely matches R(u,i). The algorithm may be run on a sample of data ina pre-training phase, and from those results it may then be extrapolatedto all data. Final scores/ratings may be calculated using randomprojection, and the top scoring concepts may then be stored for use bythe recommendation processes of social-networking system 160. Usermatrix P and concept matrix Q do not need to be trained by DSGD for allusers and all concepts. Instead, for a sample of users and all concepts,a full run of DSGD may be run to learn user matrix P and concept matrixQ from this sample. In this way concept matrix Q and concept-bias vectorB_(i)(i) may be learned from a smaller sample. These values for theconcept traits and concept offsets may then be fixed. To calculate usermatrix P for all users, repeated samples may then be chosen from the setof users without replacement. Each sample may then be used to compute asub-matrix of user matrix P corresponding to the users in the sample.This sub-matrix may be calculated by applying DSGD to the optimizationprocess described with respect to matrix factorization above, holdingconcept matrix Q and concept-bias vector B_(i)(i) fixed frompre-training. In the first training step, social-networking system 160may optimize to discover user-score vectors P(u) for each user node u,and concept-score vectors Q(i) for each concept node i on a randomsample of users P and all items Q. The concept traits can then be fixed,and social-networking system 160 may then run numerous processes on thepartitions of the user base to calculate P(u) for that user base. Theseprocesses may be run in parallel, and each parallel run may be done byrunning DSGD on a cluster of machines. As an example and not by way oflimitation, social-networking system may fix the concept trace vectorsand all biases, and use the distributed stochastic gradient descentalgorithm to train with data for the remaining 99% of users of theonline social network (assuming the first set comprised approximately 1%of users), and calculate user trace vectors for all users, concept tracevectors for all concepts, and biases for all user-concept pairs.Although this disclosure describes generating particular recommendationalgorithms in a particular manner, this disclosure contemplatesgenerating any suitable recommendation algorithm in any suitable manner.

In particular embodiments, social-networking system 160 may calculaterecommended user-concept scores for a second set of user nodes 202 ofthe plurality of nodes. The first set of user nodes 202 may be discretefrom the second set of user nodes 202. The recommended user-conceptscore may be, for example, an affinity coefficient (as discussed below),or a factor used when determining social-graph affinity. In particularembodiments, the second set of user nodes 202 may comprise substantiallyall remaining user nodes 202 of social graph 200. Social-networkingsystem 160 may take the concept traits determined by a run ofoptimization on the first set of users nodes 202, as describedpreviously, and use these to compute user traits for all otherpartitions of users of the online social network. The second set of usernodes 202 may be divided into a plurality of discrete sets of users. Asan example and not by way of limitation, the second set of user nodes202 may comprise approximately 100% of the user nodes 202 of socialgraph 200 not included in the first set of user nodes 202. For everyuser and every concept, social-networking system 160 may have a vectorthat represents the user's interest and a vector that represents theconcept's traits. As described above, along with the offsets,social-networking system 160 may quantitatively compute how much aconcept matches a user's interest by taking an inner product of the twovectors. For concept recommendations, social-networking system 160 maycompute that score for all concepts for a user, rank all concepts basedon that score, and pick the top n results. However, as discussedpreviously, with over one billion users and many million of concepts,there may be trillion computations required to estimate scores for allconcepts with respect to all users, which may be infeasible to completewithin a reasonable time frame. This problem may be solved using randomprojection (hashing). As an example and not by way of limitation,social-networking system 160 may use random projection (hashing) toproject the user trace vectors and concept trace vectors to a pluralityof sub-spaces (or buckets), such that in each sub-space, the user andconcept trace vectors have high cosine similarity (similar bit-map, orroughly pointing in the same direction). Since the user and concepttrace vectors may have high cosine similarity in a bucket, the dotproduct of user and concepts trace vectors, and thus computation of therating functions, may be carried out. The random projection may resultin only a small loss (e.g., 2%) of conversion rate. In particularembodiments, when calculating recommended user-concept scores for thesecond set of user nodes 202 of the plurality of nodes,social-networking system 160 may use a random projection process.Social-networking system 160 may calculate, for each user node of thesecond set of user nodes, a plurality of user-bias vectors B_(u)(u),wherein each user-bias vector B_(u)(u) is associated with a user node uof the second set of user nodes. Social-networking system 160 may thenmap the plurality of user-bias vectors B_(u)(u) and a plurality ofconcept-bias vectors B_(i)(i) to a plurality of sub-spaces using randomhash functions, wherein each concept-bias vector B_(i)(i) is associatedwith a concept node i of the plurality of concept nodes.Social-networking system 160 may then calculate, for each sub-space,user-concept scores for the user node u of the second set of user nodesassociated with the user-bias vector B_(u)(u) mapped to the sub-space,wherein the user-concept scores are equal to B_(u)(u)·B_(i)(i) for theuser-bias vector B_(u)(u) and the concept-bias vector B_(i)(i) mapped tothe sub-space. As an example and not by way of limitation,social-networking system 160 may define a series of random hashfunctions and use them to map each user interest vector and each conceptinterest vector to a sub-space with a sub-space ID. This process issimilar to locality sensitive hashing (LSH), and provides alow-dimensional approximation of the concept and user traits.Social-networking system 160 may then compute, for each sub-space, theinner products for all user and all concepts' vectors within the samesub-space. After this process, for any particular user and anyparticular concept, social-networking system 160 may be able tocalculate a recommended user-concept score. For every user,social-networking system 160 may rank all the concepts whose vectors arein the same sub-spate as the user's vector based on the score. The top nconcepts for that user may then be stores as recommendations for theuser. In particular embodiments, this process may be repeated atspecified time intervals so that new or updated recommendations may begenerated for each user. Although this disclosure describes calculatingparticular recommended user-concept scores in a particular manner, thisdisclosure contemplates calculating any suitable recommendeduser-concept scores in any suitable manner.

In particular embodiments, social-networking system 160 may sendrecommendations for one or more concept nodes 204 to one or more userscorresponding to the user nodes 202 of the second set of user nodes 202based on the calculated recommended user-concept scores for the secondset of user nodes 202. Based on the calculated ratings functions,social-networking system 160 may then rank the concepts with respect toeach user based on the scores and store the ranking (e.g., a list of 50top-ranked concept-profile pages) for the each user. As an example andnot by way of limitation, social-networking system 160 may recommend oneor more pages (e.g., user-profile pages or concept-profile pages) tousers of the online social network. After calculating recommendeduser-concept scores, social-networking system may, for example, send arecommendation or advertisement to a user such as, “Pages you may like”,“People you should follow”, or “Groups you should join”, where therecommendation or advertisement comprises a reference a node based onthe recommended user-concept score with respect to user receiving therecommendation or advertisement and the concept being referenced. Asanother example and not by way of limitation, the calculatedrecommended-user-concept scores may be used to calculate social-graphaffinity or affinity coefficients (as described below), which may beused as a factor when providing recommendations, advertisements, searchresults, or other suitable content for a user of an online socialnetwork. Although this disclosure describes sending particularrecommendations in a particular manner, this disclosure contemplatessending any suitable recommendations in any suitable manner.

FIG. 3 illustrates an example method 300 for determining recommendedcontent on an online social network. The method may begin at step 310,where social-networking system 160 may access a social graph comprisinga plurality of nodes and a plurality of edges 206 connecting the nodes.Each of the edges 206 between two of the nodes may represent a singledegree of separation between them. The nodes may comprise a plurality ofuser nodes 202 corresponding to a plurality of users associated with anonline social network, respectively. The nodes may also comprise aplurality of concept nodes 204 corresponding to a plurality of conceptsassociated with the online social network, respectively. At step 320,social-networking system 160 may access user-concept scores for a firstset of user nodes 202 of the plurality of nodes, respectively. Eachuser-concept score may be with respect to particular user-concept pairscomprising a user node 202 from the first set of user nodes that isconnected by an edge 206 to a concept node 204 from the plurality ofconcept nodes. At step 330, social-networking system 160 may generate arecommendation-algorithm for estimating recommended user-concept scoresfor all user-concept pairs in the first set of user nodes 202 and theplurality of concept nodes 204. The recommended user-concept scores maybe based on the accessed user-concept scores. At step 340,social-networking system 160 may calculate recommended user-conceptscores for a second set of user nodes 202 of the plurality of nodes. Thefirst set of user nodes 202 may be discrete from the second set of usernodes 202. Particular embodiments may repeat one or more steps of themethod of FIG. 3, where appropriate. Although this disclosure describesand illustrates particular steps of the method of FIG. 3 as occurring ina particular order, this disclosure contemplates any suitable steps ofthe method of FIG. 3 occurring in any suitable order. Moreover, althoughthis disclosure describes and illustrates an example method fordetermining recommended content on an online social network includingthe particular steps of the method of FIG. 3, this disclosurecontemplates any suitable method for determining recommended content onan online social network including any suitable steps, which may includeall, some, or none of the steps of the method of FIG. 3, whereappropriate. Furthermore, although this disclosure describes andillustrates particular components, devices, or systems carrying outparticular steps of the method of FIG. 3, this disclosure contemplatesany suitable combination of any suitable components, devices, or systemscarrying out any suitable steps of the method of FIG. 3.

In particular embodiments, social-networking system 160 may determinethe social-graph affinity (which may be referred to herein as“affinity”) of various social-graph entities for each other. Affinitymay represent the strength of a relationship or level of interestbetween particular objects associated with the online social network,such as users, concepts, content, actions, advertisements, other objectsassociated with the online social network, or any suitable combinationthereof. Affinity may also be determined with respect to objectsassociated with third-party systems 170 or other suitable systems. Anoverall affinity for a social-graph entity for each user, subjectmatter, or type of content may be established. The overall affinity maychange based on continued monitoring of the actions or relationshipsassociated with the social-graph entity. Although this disclosuredescribes determining particular affinities in a particular manner, thisdisclosure contemplates determining any suitable affinities in anysuitable manner.

In particular embodiments, social-networking system 160 may measure orquantify social-graph affinity using an affinity coefficient (which maybe referred to herein as “coefficient”). The coefficient may representor quantify the strength of a relationship between particular objectsassociated with the online social network. The coefficient may alsorepresent a probability or function that measures a predictedprobability that a user will perform a particular action based on theuser's interest in the action. In this way, a user's future actions maybe predicted based on the user's prior actions, where the coefficientmay be calculated at least in part a the history of the user's actions.Coefficients may be used to predict any number of actions, which may bewithin or outside of the online social network. As an example and not byway of limitation, these actions may include various types ofcommunications, such as sending messages, posting content, or commentingon content; various types of a observation actions, such as accessing orviewing profile pages, media, or other suitable content; various typesof coincidence information about two or more social-graph entities, suchas being in the same group, tagged in the same photograph, checked-in atthe same location, or attending the same event; or other suitableactions. Although this disclosure describes measuring affinity in aparticular manner, this disclosure contemplates measuring affinity inany suitable manner.

In particular embodiments, social-networking system 160 may use avariety of factors to calculate a coefficient. These factors mayinclude, for example, user actions, types of relationships betweenobjects, location information, other suitable factors, or anycombination thereof. In particular embodiments, different factors may beweighted differently when calculating the coefficient. The weights foreach factor may be static or the weights may change according to, forexample, the user, the type of relationship, the type of action, theuser's location, and so forth. Ratings for the factors may be combinedaccording to their weights to determine an overall coefficient for theuser. As an example and not by way of limitation, particular useractions may be assigned both a rating and a weight while a relationshipassociated with the particular user action is assigned a rating and acorrelating weight (e.g., so the weights total 100%). To calculate thecoefficient of a user towards a particular object, the rating assignedto the user's actions may comprise, for example, 60% of the overallcoefficient, while the relationship between the user and the object maycomprise 40% of the overall coefficient. In particular embodiments, thesocial-networking system 160 may consider a variety of variables whendetermining weights for various factors used to calculate a coefficient,such as, for example, the time since information was accessed, decayfactors, frequency of access, relationship to information orrelationship to the object about which information was accessed,relationship to social-graph entities connected to the object, short- orlong-term averages of user actions, user feedback, other suitablevariables, or any combination thereof. As an example and not by way oflimitation, a coefficient may include a decay factor that causes thestrength of the signal provided by particular actions to decay withtime, such that more recent actions are more relevant when calculatingthe coefficient. The ratings and weights may be continuously updatedbased on continued tracking of the actions upon which the coefficient isbased. Any type of process or algorithm may be employed for assigning,combining, averaging, and so forth the ratings for each factor and theweights assigned to the factors. In particular embodiments,social-networking system 160 may determine coefficients usingmachine-learning algorithms trained on historical actions and past userresponses, or data farmed from users by exposing them to various optionsand measuring responses. Although this disclosure describes calculatingcoefficients in a particular manner, this disclosure contemplatescalculating coefficients in any suitable manner.

In particular embodiments, social-networking system 160 may calculate acoefficient based on a user's actions. Social-networking system 160 maymonitor such actions on the online social network, on a third-partysystem 170, on other suitable systems, or any combination thereof. Anysuitable type of user actions may be tracked or monitored. Typical useractions include viewing profile pages, creating or posting content,interacting with content, tagging or being tagged in images, joininggroups, listing and confirming attendance at events, checking-in atlocations, liking particular pages, creating pages, and performing othertasks that facilitate social action. In particular embodiments,social-networking system 160 may calculate a coefficient based on theuser's actions with particular types of content. The content may beassociated with the online social network, a third-party system 170, oranother suitable system. The content may include users, profile pages,posts, news stories, headlines, instant messages, chat roomconversations, emails, advertisements, pictures, video, music, othersuitable objects, or any combination thereof. Social-networking system160 may analyze a user's actions to determine whether one or more of theactions indicate an affinity for subject matter, content, other users,and so forth. As an example and not by way of limitation, if a user maymake frequently posts content related to “coffee” or variants thereof,social-networking system 160 may determine the user has a highcoefficient with respect to the concept “coffee”. Particular actions ortypes of actions may be assigned a higher weight and/or rating thanother actions, which may affect the overall calculated coefficient. Asan example and not by way of limitation, if a first user emails a seconduser, the weight or the rating for the action may be higher than if thefirst user simply views the user-profile page for the second user.

In particular embodiments, social-networking system 160 may calculate acoefficient based on the type of relationship between particularobjects. Referencing the social graph 200, social-networking system 160may analyze the number and/or type of edges 206 connecting particularuser nodes 202 and concept nodes 204 when calculating a coefficient. Asan example and not by way of limitation, user nodes 202 that areconnected by a spouse-type edge (representing that the two users aremarried) may be assigned a higher coefficient than a user nodes 202 thatare connected by a friend-type edge. In other words, depending upon theweights assigned to the actions and relationships for the particularuser, the overall affinity may be determined to be higher for contentabout the user's spouse than for content about the user's friend. Inparticular embodiments, the relationships a user has with another objectmay affect the weights and/or the ratings of the user's actions withrespect to calculating the coefficient for that object. As an exampleand not by way of limitation, if a user is tagged in first photo, butmerely likes a second photo, social-networking system 160 may determinethat the user has a higher coefficient with respect to the first photothan the second photo because having a tagged-in-type relationship withcontent may be assigned a higher weight and/or rating than having alike-type relationship with content. In particular embodiments,social-networking system 160 may calculate a coefficient for a firstuser based on the relationship one or more second users have with aparticular object. In other words, the connections and coefficientsother users have with an object may affect the first user's coefficientfor the object. As an example and not by way of limitation, if a firstuser is connected to or has a high coefficient for one or more secondusers, and those second users are connected to or have a highcoefficient for a particular object, social-networking system 160 maydetermine that the first user should also have a relatively highcoefficient for the particular object. In particular embodiments, thecoefficient may be based on the degree of separation between particularobjects. The lower coefficient may represent the decreasing likelihoodthat the first user will share an interest in content objects of theuser that is indirectly connected to the first user in the social graph200. As an example and not by way of limitation, social-graph entitiesthat are closer in the social graph 200 (i.e., fewer degrees ofseparation) may have a higher coefficient than entities that are furtherapart in the social graph 200.

In particular embodiments, social-networking system 160 may calculate acoefficient based on location information. Objects that aregeographically closer to each other may be considered to be more relatedor of more interest to each other than more distant objects. Inparticular embodiments, the coefficient of a user towards a particularobject may be based on the proximity of the object's location to acurrent location associated with the user (or the location of a clientsystem 130 of the user). A first user may be more interested in otherusers or concepts that are closer to the first user. As an example andnot by way of limitation, if a user is one mile from an airport and twomiles from a gas station, social-networking system 160 may determinethat the user has a higher coefficient for the airport than the gasstation based on the proximity of the airport to the user.

In particular embodiments, social-networking system 160 may performparticular actions with respect to a user based on coefficientinformation. Coefficients may be used to predict whether a user willperform a particular action based on the user's interest in the action.A coefficient may be used when generating or presenting any type ofobjects to a user, such as advertisements, search results, news stories,media, messages, notifications, or other suitable objects. Thecoefficient may also be utilized to rank and order such objects, asappropriate. In this way, social-networking system 160 may provideinformation that is relevant to user's interests and currentcircumstances, increasing the likelihood that they will find suchinformation of interest. In particular embodiments, social-networkingsystem 160 may generate content based on coefficient information.Content objects may be provided or selected based on coefficientsspecific to a user. As an example and not by way of limitation, thecoefficient may be used to generate media for the user, where the usermay be presented with media for which the user has a high overallcoefficient with respect to the media object. As another example and notby way of limitation, the coefficient may be used to generateadvertisements for the user, where the user may be presented withadvertisements for which the user has a high overall coefficient withrespect to the advertised object. In particular embodiments,social-networking system 160 may generate search results based oncoefficient information. Search results for a particular user may bescored or ranked based on the coefficient associated with the searchresults with respect to the querying user. As an example and not by wayof limitation, search results corresponding to objects with highercoefficients may be ranked higher on a search-results page than resultscorresponding to objects having lower coefficients.

In particular embodiments, social-networking system 160 may calculate acoefficient in response to a request for a coefficient from a particularsystem or process. To predict the likely actions a user may take (or maybe the subject of) in a given situation, any process may request acalculated coefficient for a user. The request may also include a set ofweights to use for various factors used to calculate the coefficient.This request may come from a process running on the online socialnetwork, from a third-party system 170 (e.g., via an API or othercommunication channel), or from another suitable system. In response tothe request, social-networking system 160 may calculate the coefficient(or access the coefficient information if it has previously beencalculated and stored). In particular embodiments, social-networkingsystem 160 may measure an affinity with respect to a particular process.Different processes (both internal and external to the online socialnetwork) may request a coefficient for a particular object or set ofobjects. Social-networking system 160 may provide a measure of affinitythat is relevant to the particular process that requested the measure ofaffinity. In this way, each process receives a measure of affinity thatis tailored for the different context in which the process will use themeasure of affinity.

In connection with social-graph affinity and affinity coefficients,particular embodiments may utilize one or more systems, components,elements, functions, methods, operations, or steps disclosed in U.S.patent application Ser. No. 11/503,093, filed 11 Aug. 2006, U.S. patentapplication Ser. No. 12/977,027, filed 22 Dec. 2010, U.S. patentapplication Ser. No. 12/978,265, filed 23 Dec. 2010, and U.S. patentapplication Ser. No. 13/632,869, field 1 Oct. 2012, each of which isincorporated by reference.

In particular embodiments, an advertisement may be text (which may beHTML-linked), one or more images (which may be HTML-linked), one or morevideos, audio, one or more ADOBE FLASH files, a suitable combination ofthese, or any other suitable advertisement in any suitable digitalformat presented on one or more webpages, in one or more e-mails, or inconnection with search results requested by a user. In addition or as analternative, an advertisement may be one or more sponsored stories(e.g., a news-feed or ticker item on social-networking system 160). Asponsored story may be a social action by a user (such as “liking” apage, “liking” or commenting on a post on a page, RSVPing to an eventassociated with a page, voting on a question posted on a page, checkingin to a place, using an application or playing a game, or “liking” orsharing a website) that an advertiser promotes, for example, by havingthe social action presented within a pre-determined area of a profilepage of a user or other page, presented with additional informationassociated with the advertiser, bumped up or otherwise highlightedwithin news feeds or tickers of other users, or otherwise promoted. Theadvertiser may pay to have the social action promoted. As an example andnot by way of limitation, advertisements may be included among thesearch results of a search-results page, where sponsored content ispromoted over non-sponsored content.

In particular embodiments, an advertisement may be requested for displaywithin social-networking-system webpages, third-party webpages, or otherpages. An advertisement may be displayed in a dedicated portion of apage, such as in a banner area at the top of the page, in a column atthe side of the page, in a GUI of the page, in a pop-up window, in adrop-down menu, in an input field of the page, over the top of contentof the page, or elsewhere with respect to the page. In addition or as analternative, an advertisement may be displayed within an application. Anadvertisement may be displayed within dedicated pages, requiring theuser to interact with or watch the advertisement before the user mayaccess a page or utilize an application. The user may, for example viewthe advertisement through a web browser.

A user may interact with an advertisement in any suitable manner. Theuser may click or otherwise select the advertisement. By selecting theadvertisement, the user may be directed to (or a browser or otherapplication being used by the user) a page associated with theadvertisement. At the page associated with the advertisement, the usermay take additional actions, such as purchasing a product or serviceassociated with the advertisement, receiving information associated withthe advertisement, or subscribing to a newsletter associated with theadvertisement. An advertisement with audio or video may be played byselecting a component of the advertisement (like a “play button”).Alternatively, by selecting the advertisement, social-networking system160 may execute or modify a particular action of the user.

An advertisement may also include social-networking-system functionalitythat a user may interact with. As an example and not by way oflimitation, an advertisement may enable a user to “like” or otherwiseendorse the advertisement by selecting an icon or link associated withendorsement. As another example and not by way of limitation, anadvertisement may enable a user to search (e.g., by executing a query)for content related to the advertiser. Similarly, a user may share theadvertisement with another user (e.g., through social-networking system160) or RSVP (e.g., through social-networking system 160) to an eventassociated with the advertisement. In addition or as an alternative, anadvertisement may include social-networking-system context directed tothe user. As an example and not by way of limitation, an advertisementmay display information about a friend of the user withinsocial-networking system 160 who has taken an action associated with thesubject matter of the advertisement.

FIG. 4 illustrates an example computer system 400. In particularembodiments, one or more computer systems 400 perform one or more stepsof one or more methods described or illustrated herein. In particularembodiments, one or more computer systems 400 provide functionalitydescribed or illustrated herein. In particular embodiments, softwarerunning on one or more computer systems 400 performs one or more stepsof one or more methods described or illustrated herein or providesfunctionality described or illustrated herein. Particular embodimentsinclude one or more portions of one or more computer systems 400.Herein, reference to a computer system may encompass a computing device,and vice versa, where appropriate. Moreover, reference to a computersystem may encompass one or more computer systems, where appropriate.

This disclosure contemplates any suitable number of computer systems400. This disclosure contemplates computer system 400 taking anysuitable physical form. As example and not by way of limitation,computer system 400 may be an embedded computer system, a system-on-chip(SOC), a single-board computer system (SBC) (such as, for example, acomputer-on-module (COM) or system-on-module (SOM)), a desktop computersystem, a laptop or notebook computer system, an interactive kiosk, amainframe, a mesh of computer systems, a mobile telephone, a personaldigital assistant (PDA), a server, a tablet computer system, or acombination of two or more of these. Where appropriate, computer system400 may include one or more computer systems 400; be unitary ordistributed; span multiple locations; span multiple machines; spanmultiple data centers; or reside in a cloud, which may include one ormore cloud components in one or more networks. Where appropriate, one ormore computer systems 400 may perform without substantial spatial ortemporal limitation one or more steps of one or more methods describedor illustrated herein. As an example and not by way of limitation, oneor more computer systems 400 may perform in real time or in batch modeone or more steps of one or more methods described or illustratedherein. One or more computer systems 400 may perform at different timesor at different locations one or more steps of one or more methodsdescribed or illustrated herein, where appropriate.

In particular embodiments, computer system 400 includes a processor 402,memory 404, storage 406, an input/output (I/O) interface 408, acommunication interface 410, and a bus 412. Although this disclosuredescribes and illustrates a particular computer system having aparticular number of particular components in a particular arrangement,this disclosure contemplates any suitable computer system having anysuitable number of any suitable components in any suitable arrangement.

In particular embodiments, processor 402 includes hardware for executinginstructions, such as those making up a computer program. As an exampleand not by way of limitation, to execute instructions, processor 402 mayretrieve (or fetch) the instructions from an internal register, aninternal cache, memory 404, or storage 406; decode and execute them; andthen write one or more results to an internal register, an internalcache, memory 404, or storage 406. In particular embodiments, processor402 may include one or more internal caches for data, instructions, oraddresses. This disclosure contemplates processor 402 including anysuitable number of any suitable internal caches, where appropriate. Asan example and not by way of limitation, processor 402 may include oneor more instruction caches, one or more data caches, and one or moretranslation lookaside buffers (TLBs). Instructions in the instructioncaches may be copies of instructions in memory 404 or storage 406, andthe instruction caches may speed up retrieval of those instructions byprocessor 402. Data in the data caches may be copies of data in memory404 or storage 406 for instructions executing at processor 402 tooperate on; the results of previous instructions executed at processor402 for access by subsequent instructions executing at processor 402 orfor writing to memory 404 or storage 406; or other suitable data. Thedata caches may speed up read or write operations by processor 402. TheTLBs may speed up virtual-address translation for processor 402. Inparticular embodiments, processor 402 may include one or more internalregisters for data, instructions, or addresses. This disclosurecontemplates processor 402 including any suitable number of any suitableinternal registers, where appropriate. Where appropriate, processor 402may include one or more arithmetic logic units (ALUs); be a multi-coreprocessor; or include one or more processors 402. Although thisdisclosure describes and illustrates a particular processor, thisdisclosure contemplates any suitable processor.

In particular embodiments, memory 404 includes main memory for storinginstructions for processor 402 to execute or data for processor 402 tooperate on. As an example and not by way of limitation, computer system400 may load instructions from storage 406 or another source (such as,for example, another computer system 400) to memory 404. Processor 402may then load the instructions from memory 404 to an internal registeror internal cache. To execute the instructions, processor 402 mayretrieve the instructions from the internal register or internal cacheand decode them. During or after execution of the instructions,processor 402 may write one or more results (which may be intermediateor final results) to the internal register or internal cache. Processor402 may then write one or more of those results to memory 404. Inparticular embodiments, processor 402 executes only instructions in oneor more internal registers or internal caches or in memory 404 (asopposed to storage 406 or elsewhere) and operates only on data in one ormore internal registers or internal caches or in memory 404 (as opposedto storage 406 or elsewhere). One or more memory buses (which may eachinclude an address bus and a data bus) may couple processor 402 tomemory 404. Bus 412 may include one or more memory buses, as describedbelow. In particular embodiments, one or more memory management units(MMUs) reside between processor 402 and memory 404 and facilitateaccesses to memory 404 requested by processor 402. In particularembodiments, memory 404 includes random access memory (RAM). This RAMmay be volatile memory, where appropriate Where appropriate, this RAMmay be dynamic RAM (DRAM) or static RAM (SRAM). Moreover, whereappropriate, this RAM may be single-ported or multi-ported RAM. Thisdisclosure contemplates any suitable RAM. Memory 404 may include one ormore memories 404, where appropriate. Although this disclosure describesand illustrates particular memory, this disclosure contemplates anysuitable memory.

In particular embodiments, storage 406 includes mass storage for data orinstructions. As an example and not by way of limitation, storage 406may include a hard disk drive (HDD), a floppy disk drive, flash memory,an optical disc, a magneto-optical disc, magnetic tape, or a UniversalSerial Bus (USB) drive or a combination of two or more of these. Storage406 may include removable or non-removable (or fixed) media, whereappropriate. Storage 406 may be internal or external to computer system400, where appropriate. In particular embodiments, storage 406 isnon-volatile, solid-state memory. In particular embodiments, storage 406includes read-only memory (ROM). Where appropriate, this ROM may bemask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM),electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM),or flash memory or a combination of two or more of these. Thisdisclosure contemplates mass storage 406 taking any suitable physicalform. Storage 406 may include one or more storage control unitsfacilitating communication between processor 402 and storage 406, whereappropriate. Where appropriate, storage 406 may include one or morestorages 406. Although this disclosure describes and illustratesparticular storage, this disclosure contemplates any suitable storage.

In particular embodiments, I/O interface 408 includes hardware,software, or both, providing one or more interfaces for communicationbetween computer system 400 and one or more I/O devices. Computer system400 may include one or more of these I/O devices, where appropriate. Oneor more of these I/O devices may enable communication between a personand computer system 400. As an example and not by way of limitation, anI/O device may include a keyboard, keypad, microphone, monitor, mouse,printer, scanner, speaker, still camera, stylus, tablet, touch screen,trackball, video camera, another suitable I/O device or a combination oftwo or more of these. An I/O device may include one or more sensors.This disclosure contemplates any suitable I/O devices and any suitableI/O interfaces 408 for them. Where appropriate, I/O interface 408 mayinclude one or more device or software drivers enabling processor 402 todrive one or more of these I/O devices. I/O interface 408 may includeone or more I/O interfaces 408, where appropriate. Although thisdisclosure describes and illustrates a particular I/O interface, thisdisclosure contemplates any suitable I/O interface.

In particular embodiments, communication interface 410 includeshardware, software, or both providing one or more interfaces forcommunication (such as, for example, packet-based communication) betweencomputer system 400 and one or more other computer systems 400 or one ormore networks. As an example and not by way of limitation, communicationinterface 410 may include a network interface controller (NIC) ornetwork adapter for communicating with an Ethernet or other wire-basednetwork or a wireless NIC (WNIC) or wireless adapter for communicatingwith a wireless network, such as a WI-FI network. This disclosurecontemplates any suitable network and any suitable communicationinterface 410 for it. As an example and not by way of limitation,computer system 400 may communicate with an ad hoc network, a personalarea network (PAN), a local area network (LAN), a wide area network(WAN), a metropolitan area network (MAN), or one or more portions of theInternet or a combination of two or more of these. One or more portionsof one or more of these networks may be wired or wireless. As anexample, computer system 400 may communicate with a wireless PAN (WPAN)(such as, for example, a BLUETOOTH WPAN), a WI-FI network, a WI-MAXnetwork, a cellular telephone network (such as, for example, a GlobalSystem for Mobile Communications (GSM) network), or other suitablewireless network or a combination of two or more of these. Computersystem 400 may include any suitable communication interface 410 for anyof these networks, where appropriate. Communication interface 410 mayinclude one or more communication interfaces 410, where appropriate.Although this disclosure describes and illustrates a particularcommunication interface, this disclosure contemplates any suitablecommunication interface.

In particular embodiments, bus 412 includes hardware, software, or bothcoupling components of computer system 400 to each other. As an exampleand not by way of limitation, bus 412 may include an AcceleratedGraphics Port (AGP) or other graphics bus, an Enhanced Industry StandardArchitecture (EISA) bus, a front-side bus (FSB), a HYPERTRANSPORT (HT)interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBANDinterconnect, a low-pin-count (LPC) bus, a memory bus, a Micro ChannelArchitecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, aPCI-Express (PCIe) bus, a serial advanced technology attachment (SATA)bus, a Video Electronics Standards Association local (VLB) bus, oranother suitable bus or a combination of two or more of these. Bus 412may include one or more buses 412, where appropriate. Although thisdisclosure describes and illustrates a particular bus, this disclosurecontemplates any suitable bus or interconnect.

Herein, a computer-readable non-transitory storage medium or media mayinclude one or more semiconductor-based or other integrated circuits(ICs) (such, as for example, field-programmable gate arrays (FPGAs) orapplication-specific ICs (ASICs)), hard disk drives (HDDs), hybrid harddrives (HHDs), optical discs, optical disc drives (ODDs),magneto-optical discs, magneto-optical drives, floppy diskettes, floppydisk drives (FDDs), magnetic tapes, solid-state drives (SSDs),RAM-drives, SECURE DIGITAL cards or drives, any other suitablecomputer-readable non-transitory storage media, or any suitablecombination of two or more of these, where appropriate. Acomputer-readable non-transitory storage medium may be volatile,non-volatile, or a combination of volatile and non-volatile, whereappropriate.

Herein, “or” is inclusive and not exclusive, unless expressly indicatedotherwise or indicated otherwise by context. Therefore, herein, “A or B”means “A, B, or both,” unless expressly indicated otherwise or indicatedotherwise by context. Moreover, “and” is both joint and several, unlessexpressly indicated otherwise or indicated otherwise by context.Therefore, herein, “A and B” means “A and B, jointly or severally,”unless expressly indicated otherwise or indicated otherwise by context.

The scope of this disclosure encompasses all changes, substitutions,variations, alterations, and modifications to the example embodimentsdescribed or illustrated herein that a person having ordinary skill inthe art would comprehend. The scope of this disclosure is not limited tothe example embodiments described or illustrated herein. Moreover,although this disclosure describes and illustrates respectiveembodiments herein as including particular components, elements,functions, operations, or steps, any of these embodiments may includeany combination or permutation of any of the components, elements,functions, operations, or steps described or illustrated anywhere hereinthat a person having ordinary skill in the art would comprehend.Furthermore, reference in the appended claims to an apparatus or systemor a component of an apparatus or system being adapted to, arranged to,capable of, configured to, enabled to, operable to, or operative toperform a particular function encompasses that apparatus, system,component, whether or not it or that particular function is activated,turned on, or unlocked, as long as that apparatus, system, or componentis so adapted, arranged, capable, configured, enabled, operable, oroperative.

What is claimed is:
 1. A method comprising, by one or more processors ofone or more computing systems: retrieving, by one or more of theprocessors from one or more computer storage media, user-concept scoresfor a first set of users of a plurality of users, wherein theuser-concept scores are associated with previous social networkactivities of the first set of users of the plurality of users, andwherein each user-concept score is associated with a user-concept pairthat comprises a first user from the first set of users and a conceptfrom a plurality of concepts; generating, by one or more of theprocessors, a data structure comprising a concept matrix Q based on theaccessed user-concept scores of the first set of users, wherein theconcept matrix Q comprises a plurality of concept trait vectorscorresponding to the plurality of concepts, and wherein the conceptmatrix Q is fixed after being determined; selecting, by one or more ofthe processors and from the data structure, a subset of concepts of theconcept matrix Q based on a similarity metric of the plurality ofconcept trait vectors of the concept matrix Q, wherein the subset ofconcepts is associated with one or more previous social networkactivities of one or more users of a second set of users, and whereinthe second set of users is discrete from the first set of users;generating, by one or more of the processors, recommendations based onrecommended user-concept scores for a subset of user-concept pairs inthe second set of users of the plurality of users and the plurality ofconcepts based on the subset of concepts of the concept matrix Qdetermined from the first set of users, wherein the subset ofuser-concept pairs in the second set of users is a random subset ofuser-concept pairs, wherein a recommendation-algorithm computes therecommended user-concept scores for a user-concept pair by optimizing anobjective function comprising a plurality of predicted rating functions,wherein each predicted rating function is determined using a user score,a concept score, a user-bias value associated with a second user in thesecond set of users, and a concept-bias value associated with theconcept; and sending, to one or more client systems of one or more usersof the second set of users, the recommendations for one or more conceptsbased on the recommended user-concept scores for the second set ofusers.
 2. The method of claim 1, wherein retrieving the user-conceptscores for the first set of users comprises: accessing a ratings matrixR representing the user-concept scores for the first set of users; anddetermining a user matrix P based on the ratings matrix R, wherein theuser matrix P comprises a plurality of user-score vectors P(u) for eachuser u of the first set of users; and determining the concept matrix Qbased on the ratings matrix R, wherein the concept matrix Q comprises aplurality of concept-score vectors Q(i) for each concept i of theplurality of concepts.
 3. The method of claim 2, wherein the user matrixP, the user-score vectors P(u) for each user u, the concept matrix Q,and the concept-score vectors Q(i) for each concept i are determinedusing distributed stochastic gradient descent.
 4. The method of claim 1,wherein generating the recommendations based on the recommendeduser-concept scores further comprises: accessing a user matrix Pcomprising a plurality of user-score vectors P(u) for each user u of thefirst set of users, wherein each user u is associated with a user-biasvector B_(u) (u); accessing the concept matrix Q comprising a pluralityof concept-score vectors Q(i) for each concept i of the plurality ofconcepts, wherein each concept i is associated with a concept-biasvector B_(i)(i); and generating an estimator matrix R′ representingrecommended user-concept scores for the first set of users, whereinR′(u,i)=P(u)·Q(i)+B_(u)(u)+B_(i)(i) for each user-concept pair.
 5. Themethod of claim 1, wherein generating the recommendations based on therecommended user-concept scores further comprises: calculating, for eachuser of the second set of users, a plurality of user-bias vectorsB_(u)(u), wherein each user-bias vector B_(u)(u) is associated with auser u of the second set of users; mapping the plurality of user-biasvectors B_(u)(u) and a plurality of concept-bias vectors B_(i)(i) to aplurality of sub-spaces using one or more random hash functions, whereineach concept-bias vector B_(i)(i) is associated with a concept i of theplurality of concepts; and calculating, for each sub-space, user-conceptscores for the user u of the second set of users associated with theuser-bias vector B_(u)(u) mapped to the sub-space, wherein theuser-concept scores are equal to B_(u)(u)·B_(i)(i)for the user-biasvector B_(u)(u) and the concept-bias vector B_(i)(i) mapped to thesub-space.
 6. The method of claim 5, wherein mapping the plurality ofuser-bias vectors B_(u)(u) and the plurality of concept-bias vectorsB_(i)(i) to a plurality of sub-spaces using the random hash functionscomprises using a random projection process to project the plurality ofuser-bias vectors B_(u)(u) and a plurality of concept-bias vectorsB_(i)(i) to the plurality of sub-spaces.
 7. The method of claim 1,wherein generating the recommendations based on the recommendeduser-concept scores for the second set of users is performed on aplurality of discrete sets of users from the second set of users usingdistributed stochastic gradient descent on the one or more processors ofthe one or more computing systems.
 8. The method claim 1, wherein thefirst set of users comprises a representative sample of users of anonline social network.
 9. The method claim 1, wherein the first set ofusers comprises approximately 1% of the users of an online socialnetwork.
 10. The method of claim 1, wherein the second set of userscomprises substantially all remaining users of an online social network.11. The method of claim 1, wherein the second set of users comprisesapproximately 100% of the users of an online social network minus thefirst set of users.
 12. The method of claim 11, wherein the second setof users is divided into a plurality of discrete sets of users.
 13. Themethod of claim 1, further comprising: accessing a social graphcomprising a plurality of nodes and a plurality of edges connecting thenodes, each of the edges between two of the nodes representing a singledegree of separation between them, the nodes comprising: a plurality ofuser nodes corresponding to the plurality of users, respectively; and aplurality of concept nodes corresponding to the plurality of concepts,respectively.
 14. The method of claim 13, further comprisingcalculating, for each user-concept pair, an affinity coefficient betweenthe user node and the concept node that correspond to the respectiveuser-concept pair, wherein the affinity coefficient is based at least inpart on the recommended user-concept score for the respectiveuser-concept pair.
 15. The method of claim 14, wherein sending therecommendations for one or more concepts is further based on thecalculated affinity coefficients.
 16. The method of claim 13, whereineach edge of the plurality of edges comprises a particular edge-typecorresponding to a particular action a third user performed with respectto a concept.
 17. The method of claim 16, further comprisingcalculating, for each user-concept pair, an affinity coefficient betweenthe user node and the concept node that correspond to the respectiveuser-concept pair, wherein the affinity coefficient is based at least inpart on the particular edge-type of the edge that connects the user nodeto the concept node.
 18. One or more computer-readable non-transitorystorage media embodying software that is operable when executed to:retrieve, by one or more of the processors from one or more computerstorage media, user-concept scores for a first set of users of aplurality of users, wherein the user-concept scores are associated withprevious social network activities of the first set of users of theplurality of users, and wherein each user-concept score is associatedwith a user-concept pair that comprises a first user from the first setof users and a concept from a plurality of concepts; generate, by one ormore of the processors, a data structure comprising a concept matrix Qbased on the accessed user-concept scores of the first set of users,wherein the concept matrix Q comprises a plurality of concept traitvectors corresponding to the plurality of concepts, and wherein theconcept matrix Q is fixed after being determined; select, by one or moreof the processors and from the data structure, a subset of concepts ofthe concept matrix Q based on a similarity metric of the plurality ofconcept trait vectors of the concept matrix Q, wherein the subset ofconcepts is associated with one or more previous social networkactivities of one or more users of a second set of users, and whereinthe second set of users is discrete from the first set of users;generate, by one or more of the processors, recommendations based onrecommended user-concept scores for a subset of user-concept pairs inthe second set of users of the plurality of users and the plurality ofconcepts based on the subset of concepts of the concept matrix Qdetermined from the first set of users, wherein the subset ofuser-concept pairs in the second set of users is a random subset ofuser-concept pairs, wherein a recommendation-algorithm computes therecommended user-concept scores for a user-concept pair by optimizing anobjective function comprising a plurality of predicted rating functions,wherein each predicted rating function is determined using a user score,a concept score, a user-bias value associated with a second user in thesecond set of users, and a concept-bias value associated with theconcept; and send, to one or more client systems of one or more users ofthe second set of users, the recommendations for one or more conceptsbased on the recommended user-concept scores for the second set ofusers.
 19. A system comprising: one or more processors; and a memorycoupled to the processors comprising instructions executable by theprocessors, the processors operable when executing the instructions to:retrieve, by one or more of the processors from one or more computerstorage media, user-concept scores for a first set of users of aplurality of users, wherein the user-concept scores are associated withprevious social network activities of the first set of users of theplurality of users, and wherein each user-concept score is associatedwith a user-concept pair that comprises a first user from the first setof users and a concept from a plurality of concepts; generate, by one ormore of the processors, a data structure comprising a concept matrix Qbased on the accessed user-concept scores of the first set of users,wherein the concept matrix Q comprises a plurality of concept traitvectors corresponding to the plurality of concepts, and wherein theconcept matrix Q is fixed after being determined; select, by one or moreof the processors and from the data structure, a subset of concepts ofthe concept matrix Q based on a similarity metric of the plurality ofconcept trait vectors of the concept matrix Q, wherein the subset ofconcepts is associated with one or more previous social networkactivities of one or more users of a second set of users, and whereinthe second set of users is discrete from the first set of users;generate, by one or more of the processors, recommendations based onrecommended user-concept scores for a subset of user-concept pairs inthe second set of users of the plurality of users and the plurality ofconcepts based on the subset of concepts of the concept matrix Qdetermined from the first set of users, wherein the subset ofuser-concept pairs in the second set of users is a random subset ofuser-concept pairs, wherein a recommendation-algorithm computes therecommended user-concept scores for a user-concept pair by optimizing anobjective function comprising a plurality of predicted rating functions,wherein each predicted rating function is determined using a user score,a concept score, a user-bias value associated with a second user in thesecond set of users, and a concept-bias value associated with theconcept; and send, to one or more client systems of one or more users ofthe second set of users, the recommendations for one or more conceptsbased on the recommended user-concept scores for the second set ofusers.
 20. The method of claim 1, wherein the concept matrix Q comprisesa plurality of concept-score vectors Q(i) for each concept i of theplurality of concepts, wherein each concept i is associated with auser-bias vector B_(u)(u).
 21. The method of claim 1, wherein theconcept matrix Q is based on a ratings matrix R representing theuser-concept scores for the first set of users.
 22. The method of claim21, wherein the concept matrix Q is determined using distributedstochastic gradient descent (DSGD).
 23. The method of claim 1, whereinthe concept matrix Q is fixed and used to calculate a user matrix P byapplying distributed stochastic gradient descent (DSGD) to anoptimization process of a matrix factorization.